Here is information are my various research papers, lecture handouts, textbooks, and so on.

Textbooks#

• Euclidean Geometry in Mathematical Olympiads. 300 pages, published under MAA Problem Book Series (by the AMS).

• An Infinitely Large Napkin, higher math introduction. Nearing 1000 pages.

• 18.02 course notes, textbook for MIT’s multivariable calculus course, published under MIT OpenCourseWare.

PhD thesis#

Some materials related to my PhD thesis:

• Thesis PDF
  • MIT Libraries version (has more typos)
• Slides from my thesis defense
• Notes from pre-quals (not polished or edited, so rough and likely non-useful)
• Source code for all files
• Accompanying arXiv paper (subset of thesis)

Research publications#

Here is a listing of all my papers on arXiv. I’m also MR Author ID 1158569 and ORCID 0000-0001-9550-5068.

• arXiv:1709.05753.
  A family of partially ordered sets with small balance constant.
  E. Chen. Electronic Journal of Combinatorics.

• arXiv:2602.05090.
  Almost all primes are partially regular.
  arXiv preprint.

• arXiv:1608.04146.
  Avoiding algebraic integers of bounded house in orbits of rational functions over cyclotomic closures.
  E. Chen. Proceedings of the AMS.

• arXiv:1507.07122.
  Elliptic curve variants of the least quadratic nonresidue problem and Linnik’s Theorem.
  E. Chen, P. Park, and A. Swaminathan. Intl Journal of Number Theory.

• arXiv:2602.03716.
  Fel’s Conjecture on Syzygies of Numerical Semigroups.
  arXiv preprint.

• arXiv:2411.04872.
  FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI.
  arXiv preprint.

• arXiv:1609.01247.
  Linear polychromatic colorings of hypercube faces.
  E. Chen. Electronic Journal of Combinatorics.

• arXiv:1506.09170.
  Linnik’s Theorem on Sato-Tate Laws on elliptic curves with complex multiplication.
  E. Chen, P. Park, and A. Swaminathan. Research in Number Theory.

• arXiv:1710.02734.
  Multiplicative and exponential orthomorphisms.
  E. Chen. Journal of Combinatorics.

• arXiv:1507.02629.
  On Logarithmically Benford Sequences.
  E. Chen, P. Park, and A. Swaminathan. Proceedings of the AMS.

• arXiv:2602.03722.
  Parity of k-differentials in genus zero and one.
  arXiv preprint.

• arXiv:1708.01350.
  Schur-concavity for avoidance of increasing subsequences in block-ascending permutations.
  E. Chen. Electronic Journal of Combinatorics.

• arXiv:2502.06078.
  Semi-Lie arithmetic fundamental lemma for the full spherical Hecke algebra.
  arXiv preprint.

• arXiv:1609.04626.
  The 26 Wilf-equivalence classes of length five quasi-consecutive patterns.
  E. Chen, S. Narayanam. Discrete Math and Theoretical CS.

High school lectures#

In high school I would often give lectures and talks at math circles and the like. These are in general easier than my Olympiad handouts. They also tend to omit many details (after all, the handout usually accompanies a two-hour talk). I’ve included notes for these here.

To compile these documents in LaTeX, you will need evan.sty.

Berkeley Math Circle – Advanced group#

• AMC 12 Preparation (pdf) (tex)
  TeX source contains answers.

• Barycentric Coordinates (pdf) (tex)
  A quick introduction to barycentric coordinates.

• Combinatorial Nullstellensatz (pdf) (tex)
  Applies the combinatorial nullstellensatz to several olympiad-style problems.

Berkeley Math Circle – Intermediate II group#

• Triangle Centers (pdf) (tex)
  Standard fare on the Euler line and the nine-point circle. Might be interesting to people starting out on olympiad geometry.

• Set Theory (pdf) (tex)
  Talked about ZFC and the construction of the ordinals. Essentially equivalent to this blog post of mine.

• Parallelograms (pdf) (tex)
  All you have to do is construct a parallelogram! Some terse solutions outlined here.

• BAMO Preparation (pdf) (tex)
  A combinatorially flavored practice session for the Bay Area Math Olympiad.

Miscellaneous#

• Combinatorial Nullstellensatz (SPARC) (pdf) (tex)
  Slides from an informal lecture I gave on the nullstellensatz at SPARC 2013.